Martin Aigner Book order

The book explores the Theorem of Markov and its Uniqueness Conjecture within number theory, revealing intricate connections along the way. It guides readers through a mathematical journey that culminates in a comprehensive proof of the theorem, showcasing the elegance and coherence of the concepts involved.

Focusing on the evolution of combinatorics as a distinct branch of discrete mathematics, this book addresses its scope and organization, dividing the field into enumeration and order theory. It delves into topics like generating functions, finite posets, and existence results, while intentionally excluding configurations due to the availability of existing literature. The author aims to fill the gap in comprehensive resources for enumeration and order theory, offering a detailed exploration of these foundational aspects of combinatorics.

The authors are renowned mathematicians; their presentations cover a wide range of topics. From compact discs to the stock exchange, from computer tomography to traffic routing, from electronic money to climate change, they make the "math inside" understandable and enjoyable.

Combinatorial enumeration is a readily accessible subject full of easily stated, but sometimes tantalizingly difficult problems. This book leads the reader in a leisurely way from the basic notions to a variety of topics, ranging from algebra to statistical physics. Its aim is to introduce the student to a fascinating field, and to be a source of information for the professional mathematician who wants to learn more about the subject. The book is organized in three parts: Basics, Methods, and Topics. There are 666 exercises, and as a special feature every chapter ends with a highlight, discussing a particularly beautiful or famous result.

The advent of fast computers and the search for efficient algorithms revolutionized combinatorics and brought about the field of discrete mathematics. This book is an introduction to the main ideas and results of discrete mathematics, and with its emphasis on algorithms it should be interesting to mathematicians and computer scientists alike. The book is organized into three parts: enumeration, graphs and algorithms, and algebraic systems. There are 600 exercises with hints and solutions to about half of them. The only prerequisites for understanding everything in the book are linear algebra and calculus at the undergraduate level. Praise for the German edition ... This book is a well-written introduction to discrete mathematics and is highly recommended to every student of mathematics and computer science as well as to teachers of these topics. --Konrad Engel for MathSciNet Martin Aigner is a professor of mathematics at the Free University of Berlin. He received his PhD at the University of Vienna and has held a number of positions in the USA and Germany before moving to Berlin. He is the author of several books on discrete mathematics, graph theory, and the theory of search. The Monthly article Turan's graph theorem earned him a 1995 Lester R. Ford Prize of the MAA for expository writing, and his book Proofs from the BOOK with Gunter M. Ziegler has been an international success with translations into 12 languages.

The mathematical heroes of this book are "perfect proofs": ideas, connections and observations that bring insight and surprising perspectives on basic and challenging problems, from number theory, geometry, analysis, combinatorics, and graph theory. Thirty examples are presented here.